Question

Cos theta.cosec theta - sin theta .sec theta/ cos theta + sin theta= cosec theta - sec theta

Answer 1

Answer:

your answer attached in the photo

Answer 2

$LHS =\red{\frac{cos \theta Cosec \theta - sin \theta sec \theta }{cos \theta + sin \theta }}$

$= \frac{cos \theta \times \frac{1}{sin \theta} - sin \theta \frac{1}{ cos \theta }}{(cos \theta + sin \theta) }$

$= \frac{ \frac{ cos^{2} \theta - sin^{2} \theta }{cos \theta sin \theta }}{ ( cos \theta + sin \theta ) }$

$= \frac{( cos^{2} \theta - sin^{2} \theta) }{cos \theta sin \theta ( cos \theta + sin \theta ) }$

$= \frac{( cos \theta - sin\theta)\cancel {(cos \theta + sin \theta )} }{cos \theta sin \theta \cancel {( cos \theta + sin \theta )} }$

$= \frac{ cos \theta - sin \theta }{cos \theta sin \theta }$

$= \frac{cos \theta}{cos \theta sin \theta} - \frac{sin \theta}{ cos \theta sin \theta }$

$= \frac{1 }{ sin \theta} - \frac{1}{ cos \theta}$

$\green {= Cosec \theta - Sec \theta }$

$= RHS$

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